Determining Number of Maxima: 2 Slits & 500 nm Light

In summary, using the formula dsinθ = m(lambda), the number of maxima observed in the angular range of -31.0° < θ < +31.0° for a beam of 500 nm light passing through two slits separated by 0.260 mm is 536.
  • #1
hodgepodge
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0

Homework Statement


Two slits are separated by 0.260 mm. A beam of 500 nm light strikes the slits, producing an interference pattern. Determine the number of maxima observed in the angular range -31.0° < θ < +31.0°.


Homework Equations


i used dsinθ = m(lambda)


The Attempt at a Solution


i used the formula above and got
(.26 x 10^-3)sin(31) = m (500 x 10^-9)

i got m as 267.82, but since there are 267.82 maxima to the right, and 267.82 to the left and one at m=0, that makes for a total number of 536.64 maxima

?
 
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  • #2
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i need to know what if i did anything wrong, or if the book is wrong
 
  • #3
Hello hodgepodge.The number of maxima must be a whole number eg you may get 267 maxima on one side but not 267.82.
 
  • #4
werd, thanks
 

Related to Determining Number of Maxima: 2 Slits & 500 nm Light

1. How do you determine the number of maxima in a double slit experiment with 500 nm light?

In order to determine the number of maxima in a double slit experiment with 500 nm light, you will need to use the equation N = d/λ, where N is the number of maxima, d is the distance between the two slits, and λ is the wavelength of the light. You can also use the equation N = (2w/λ)(tanθ), where w is the width of the slits and θ is the angle of diffraction.

2. What is the significance of the wavelength of light in determining the number of maxima?

The wavelength of light is a crucial factor in determining the number of maxima in a double slit experiment. This is because the spacing between the maxima is directly proportional to the wavelength of the light. As the wavelength decreases, the spacing between the maxima also decreases, resulting in a higher number of maxima.

3. Can the width of the slits affect the number of maxima in a double slit experiment?

Yes, the width of the slits can affect the number of maxima in a double slit experiment. As the width of the slits decreases, the number of maxima increases. This is because narrower slits result in a higher diffraction at the edges, creating more maxima.

4. How does the distance between the two slits impact the number of maxima in a double slit experiment?

The distance between the two slits, also known as the slit spacing, is directly proportional to the number of maxima in a double slit experiment. As the distance between the slits increases, the number of maxima decreases. This is because a larger slit spacing results in a wider diffraction pattern, leading to fewer maxima.

5. Is the number of maxima affected by the intensity of the light used in a double slit experiment?

No, the intensity of the light does not affect the number of maxima in a double slit experiment. The intensity only affects the brightness of the maxima, but not their number or spacing. This is because the number of maxima is determined by the wavelength, slit spacing, and slit width, which are all constant for a given experiment.

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